Binary Source Lensing and the Repeating OGLE EWS Events

The shape of the microlensing light curve may be changed if the observed source is a binary star. In particular the event may look as subsequent two events corresponding to microlensing of two binary components. The probability of observing a binary source microlensing has been investigated theoretically by several authors (Griest and Hu, 1992;Dominik, 1998;Han and Jeong, 1998;Han 2005, to cite few). The typical conclusion of such studies is that in few percent of cases where the source is a binary, this fact should have observable consequences. Assuming that the stars in the Galactic bulge form binary systems with probability similar to the stars in the disk (which has not been proved), one expects that several tens of events among several thousands discovered to date have binary source characteristics.

In a recent paper Skowron et al. (2009) investigate the problem of repeating microlensing events using the data of the Optical Gravitational Lens Experiment (e.g., Udalski 2003). Majority of the events have been discovered by the Early Warning System (EWS -see Udalski et al. 1994;Udalski 2003 for details). The definition of an repeating microlensing event adopted by Skowron et al. requires that the two brightenings in the light curve caused by microlensing are well separated, i.e. the observed luminosity comes to the baseline between the peaks. There are 19 such cases among 4120 events investigated, and 12 of them are interpreted as a result of lensing by wide binary systems, while 6 allow concurrent binary lens/binary source interpretations. Even if all ambiguous cases were binary source events, the probability of observing a binary source repeating event would be only 0.15%.

Not all the binary source events comply with the above definition of repeating events. If the binary source separation is of the order of the lens Einstein radius, the peaks in the light curve partially overlap. This may produce smooth light curves of various shapes, some indistinguishable from those produced by single source approaching cusps of the binary lens caustics. Even the binary lens caustic crossing event may be classified as due to binary source if the observations are sparse. Examples of several binary source / binary lens events are given by Jaroszyński et al. (2004,2006) and Skowron et al. (2007).

In this paper we simulate the microlensing light curves with binary sources to find probability of producing a repeating event. Our aim is to obtain realistic light curves, and we include several details typical for the OGLE team observations. (Sampling rates, observational errors and their dependence on observed luminosity, span of observations etc). Also the classification of simulated light curves and fitting procedures closely follow the approach of Skowron et al. (2009). We expect, that the probability of finding a repeating event among simulated light curves would be directly comparable with the number obtained as a result of analyzing all EWS events by Skowron et al. (2009), and some limits on the binary stars population in the Galactic bulge will be possible to place.

A binary source event light curve can be modeled using eight parameters: the times of closest approaches of the lens to the source components t 01 and t 02 , the characteristic Einstein time t E , the two dimensionless impact parameters b 1 and b 2 , the two source components energy fluxes F 1 and F 2 , and the blended flux of stars in the seeing disk F b . The observed flux is a given function of time:

where A(u) describes the so called Paczyński curve (e.g. Paczyński, 1991):

The model parameters listed above are related to even larger number of parameters characterizing the lens and source distances d L , d S , lens mass m, observer, lens and source velocities v O , v L , v S , and source components intrinsic luminosities L 1 , L 2 . The Einstein time is is given as

where r E is the Einstein radius and v ⊥ is the velocity of the lens relative to the line joining the observer and the source, measured in the plane perpendicular to this line:

The Einstein radius is a unit of length in the lens plane; in the source plane the projected Einstein radius rE ≡ r E /x plays the same role. The shape of the light curve depends on the binary source separation or, more precisely, on the projected into the sky distance between the two components in the time of interest, expressed in Einstein radius units, d ≡ a ⊥ /r E . Since we investigate a population of binary sources with large scatter of separations and the microlensing events may happen in any phase of b

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